class of the language

Question

Let Σ = {a, b}. For a word w ∈ Σ* , let n_a(x) denote the number of a’s in w and let n_b(x) denote the number of b’s in w. Consider the following language: 
L := {xy | x, y ∈ Σ* , n_a(x) = n_b(y)} 
What can we say about L?

	(A) L is regular, but not context-free.
	(B) L is context-free, but not regular.
	(C) L is Σ*.
	(D) None of these.

Comments

Yes given option is right. It contains all strings.

Like for string  $a   \epsilon L  $ , $ x$ part  is $\lambda$ and $y $ part is $a$ so $n_a(x) =0=n_b(y)$.

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can u explain in more detail??

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X concatenate with y and both x and y belongs to  Σ*,

So language will become  Σ*.

Answer 1

https://gateoverflow.in/170462/class-of-the-languages